Solving Turbulent Rayleigh-B\'enard Convection using Fourier Neural Operators

TL;DR

This paper demonstrates that Fourier Neural Operators can accurately and efficiently model turbulent Rayleigh-Bénard Convection, outperforming traditional methods and enabling zero-shot super-resolution for fluid dynamics applications.

Contribution

The study introduces FNO as a novel surrogate model for RBC, showing superior accuracy and speed, and highlights its zero-shot super-resolution capability.

Findings

FNO outperforms DMD and LRAN in accuracy and speed

FNO demonstrates zero-shot super-resolution in convection dynamics

FNO has potential for downstream flow control tasks

Abstract

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO surrogates to two popular surrogates used in fluid dynamics: the Dynamic Mode Decomposition and the Linearly-Recurrent Autoencoder Network. We regard Direct Numerical Simulations (DNS) of the RBC equations as the ground truth on which the models are trained and evaluated in different settings. The FNO performs favorably when compared to the DMD and LRAN and its predictions are fast and highly accurate for this task. Additionally, we show its zero-shot super-resolution ability for the convection dynamics. The FNO model has a high potential to be used in downstream tasks such as flow control in RBC.